Do I have to unwrap the cup again?
Screenshot 1 To see the UV maps do the following...

select the object in the outliner. You can select more than one object if you want to unwrap them on the same UV map
switch to Edit Mode
make sure you have selected the correct UV map
select the faces you want to see. Press A to select them all and it should reveal the whole UV map. You can unwrap the object(s) with U. The Unwrap operation requires seams (the red lines). Smart UV Project does not need seams.
in the UV editor you can see the UV islands now. If you select only a few faces in the viewport then only those are shown here. You can drag them around and they will become separated islands. This way you don't need a seam.
if you're looking for a specific face you can activate the UV Sync Selection mode. In this mode, any face you select in the UV editor will be selected in the viewport and vice versa. Tip: Use Face Selection mode (3). In this mode, vertices of connected islands are automatically selected. Turn sync off, if you want to move a UV island.


Screenshot 2

here in the section Object Data Properties &gt; UV Maps, you can select the UV map that you want to edit. The camera icon specifies the map that is used for the render. In this list, you can also add more UV maps and delete unnecessary ones.

In the Image Editor on the left, you can select an image that is displayed for the UV map.